求导数:(2) y=(1-x)(1-2x) (4) y=(2+3x^2)√(1+〖5x〗^2 ) (8) y=log⁡a(1+x^2)

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求导数:(2) y=(1-x)(1-2x) (4) y=(2+3x^2)√(1+〖5x〗^2 ) (8) y=log⁡a(1+x^2)

求导数:(2) y=(1-x)(1-2x) (4) y=(2+3x^2)√(1+〖5x〗^2 ) (8) y=log⁡a(1+x^2)
求导数:(2) y=(1-x)(1-2x) (4) y=(2+3x^2)√(1+〖5x〗^2 ) (8) y=log⁡a(1+x^2)

求导数:(2) y=(1-x)(1-2x) (4) y=(2+3x^2)√(1+〖5x〗^2 ) (8) y=log⁡a(1+x^2)
(2)y'=[(1-x)(1-2x)]'=(1-x)'(1-2x)+(1-x)(1-2x)'=-(1-2x)-2(1-x)=4x-3
(4)y'=6x[1+(5x)^2 ]^0.5 + 0.5[1+(5x)^2]'(2+3x^2)[1+(5x)^2]^(-0.5)
=6x[1+(5x)^2 ]^0.5 + 0.5*2*5x*(5x)'(2+3x^2)[1+(5x)^2]^(-0.5)
=6x[1+(5x)^2 ]^0.5 + 25x(2+3x^2)[1+(5x)^2]^(-0.5)
(8)y'=[ln(1+x^2)/lna]'=(x^2)'/(1+x^2)lna=2x/(1+x^2)lna